These are names for a stringed instrument of the 17th century,
a type of bass archlute.
The organ stop, supposedly imitative of the instrument, has been
made in four varieties:

(1) A rare German reed stop of the 17th and 18th centuries,
described by Grove as “a distinct type, i.e. a gentle 16' tone”.
According to Maclean, it was made by builders such as Casparini,
Engler, and Mosengel.

(2) A Spanish reed with short resonators, called “more familiar”
by Grove and “more important” by Williams, dating from around 1750
and often found en chamade.
Maclean puts it at 16' or 8' pitch, on the treble half of the split
Spanish manual.

(3) According to Williams, “a string stop similar to the other
narrow flue ranks popular at the end of the 18th cent.”

(4) A mixture of II or III ranks. While not mentioned in the literature,
most of the known examples are of this variety.

Examples

No examples of the names Theorbo or Tiorba are known.
Contributions welcome.
Osiris contains nine examples of Theorbe,
all appearing in pedal divisions.
From their position in the stop-lists, two appear to be flues,
not reeds. The other seven are mixtures of II or III ranks.

Theorba 16'; Görlitz; Casparini 1695.
Cited by Grove and Williams.

Theorba 16'; Königsberg Cathedral; Mosengel 1721.
A reed stop.

Theorbe 16', Pedal; Lorenzkirche, Nürnberg,
Germany; Steinmeyer 1937. (From its position in the stop list,
this example appears to be a flue.)